The Bundesliga champions put eight past Hamburg last weekend and threatened to equal that scoreline in another emphatic attacking display.
Lewandowski marked his recall to the starting XI, in place of Mario Gotze, with two goals in a first half of few chances.
And Bayern picked off the hosts almost at will following the dismissal of Paderborn's Florian Hartherz in the 62nd minute, as Robben scored twice either side of Franck Ribery and substitute Mitchell Weiser.
Paderborn remain in a position of great danger near the foot of the table, while Bayern hold an 11-point advantage at the summit ahead of second-placed Wolfsburg's meeting with Hertha Berlin on Sunday.
The visitors dominated possession from the outset, but were unable to fashion a clear sight of goal early on as Paderborn, adopting a 5-4-1 formation, packed men behind the ball and defended with discipline.
A 12th-minute counter-attack from Paderborn ended with Alban Meha sending an ambitious long-range effort narrowly wide of Manuel Neuer's left-hand post.
However, Andre Breitenreiter's side fell behind 12 minutes later as Lewandowski converted Bayern's first chance of the game.
Robben was the creator, cleverly flicking on David Alaba's pass with a deft touch that enabled Lewandowski to run in on goal unchallenged before placing his finish through the legs of goalkeeper Lukas Kruse.
Lewandowski also accepted the next opportunity that came Bayern's way, prodding home a Ribery cross at the near post eight minutes before half-time after a shot from Thomas Muller had deflected into the path of the Frenchman.
Neuer was called upon to make a routine save from the recalled Lukas Rupp prior to the interval, while Robben saw a shot flash wide at the other end.
Holger Badstuber, who lined up alongside Jerome Boateng at the heart of Bayern's defence following the latter's recent suspension, made a fine last-ditch tackle to deny Elias Kachunga as Paderborn started the second half brightly.
There was little else to concern Bayern, however, and their afternoon became much easier when Hartherz clumsily felled Robben as the forward attempted to convert a left-wing cross, earning a red card as a result.
Robben made no mistake with the resulting spot-kick and a fourth goal arrived in the 72nd minute when Ribery drilled home a first-time shot from 15 yards.
Weiser added a fifth two minutes after his 76th-minute introduction, lobbing Kruse for his first Bundesliga goal, and Robben capped off a thoroughly one-sided fixture by applying a finish to Ribery's cross with four minutes remaining.